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>So... Yes, these are both (special cases of) magmas, but the general term used for them is "algebra" or "algebraic structure". Don't you agree?

Algebraic stucture, sure, but _algebra_, absolutely not.

An algebra is a module with a compatible multiplication which has an identity element. If I had a magma and you asked about my "algebra" I would be very confused about where you were seeing all the extra structure.

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> Algebraic stucture, sure, but _algebra_, absolutely not.

As someone else pointed out elsethread, the term seems to be overloaded in different branches of mathematics.

https://en.wikipedia.org/wiki/Universal_algebra: "Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. [...] In universal algebra, an algebra (or algebraic structure) is a set A together with a collection of operations on A."

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